Finite-automaton transformations of strictly almost-periodic sequences
Matematičeskie zametki, Tome 80 (2006) no. 5, pp. 751-756
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Different versions of the notion of almost-periodicity are natural generalizations of the notion of periodicity. The notion of strict almost-periodicity appeared in symbolic dynamics, but later proved to be fruitful in mathematical logic and the theory of algorithms as well. In the paper, a class of essentially almost-periodic sequences (i.e., strictly almost-periodic sequences with an arbitrary prefix added at the beginning) is considered. It is proved that the property of essential almost-periodicity is preserved under finite-automaton transformations, as well as under the action of finite transducers. The class of essentially almost-periodic sequences is contained in the class of almost-periodic sequences. It is proved that this inclusion is strict.
@article{MZM_2006_80_5_a9,
author = {Yu. L. Pritykin},
title = {Finite-automaton transformations of strictly almost-periodic sequences},
journal = {Matemati\v{c}eskie zametki},
pages = {751--756},
publisher = {mathdoc},
volume = {80},
number = {5},
year = {2006},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_2006_80_5_a9/}
}
Yu. L. Pritykin. Finite-automaton transformations of strictly almost-periodic sequences. Matematičeskie zametki, Tome 80 (2006) no. 5, pp. 751-756. http://geodesic.mathdoc.fr/item/MZM_2006_80_5_a9/